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Failure of Rational Dilation on the Tetrablock via Parrott Homomorphisms
We determine the cotangent operator space structure at the origin of the tetrablock (denoted by $\mathbb E$). In particular we prove that $\operatorname{COT}_0(\overline{\mathbb E}) =\operatorname{MIN}(\ell_1^2\oplus_\infty\mathbb C)$ completely isometrically. This shows the existence of commuting
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